Why can't I just add ng-app to the body tag?

Angular looks for ng-app attributes and works its magic once the document is ready. However, so does GoldenLayout. So in order to make the two work together you have to follow these three steps:

Create a Layout with GoldenLayout

Load your templates into GoldenLayout's containers

Bootstrap Angular

Creating the layout

This one should be fairly straight forward by now. If not, have a look at the getting started tutorial. Two container, side by side, without headers.
The only thing note-worthy is the { templateId: 'userNameTemplate' } bit. This will be used to tell our component which template to load.

Loading Templates

For this example we'll store our html in template tags. (Not supported in IE). This is only one of many ways to store and retrieve pieces of html. You could also use Angular's $templateCache or ng-include method, RequireJS' text plugin, hidden divs, Ajax or a number of other approaches.